Solve for $x$ and $y$ using elimination. ${-2x-3y = -30}$ ${-5x-y = -23}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${-2x-3y = -30}$ $15x+3y = 69$ Add the top and bottom equations together. $13x = 39$ $\dfrac{13x}{{13}} = \dfrac{39}{{13}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-2x-3y = -30}\thinspace$ to find $y$ ${-2}{(3)}{ - 3y = -30}$ $-6-3y = -30$ $-6{+6} - 3y = -30{+6}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-5x-y = -23}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ - y = -23}$ ${y = 8}$